CN111351425A - Method for determining dynamic range of interferometer during spherical defocus detection - Google Patents

Method for determining dynamic range of interferometer during spherical defocus detection Download PDF

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CN111351425A
CN111351425A CN202010161017.0A CN202010161017A CN111351425A CN 111351425 A CN111351425 A CN 111351425A CN 202010161017 A CN202010161017 A CN 202010161017A CN 111351425 A CN111351425 A CN 111351425A
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interferometer
detector
spherical
dynamic range
interference
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CN111351425B (en
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潘宝珠
汤靖
王雪莹
方靖淮
姜舒昊
仲崇贵
纪宪明
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Nantong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B9/00—Measuring instruments characterised by the use of optical techniques
    • G01B9/02—Interferometers
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
    • G01B11/2441—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures using interferometry

Abstract

The invention provides a method for determining the dynamic range of an interferometer in spherical defocus detection, wherein the dynamic range of the interferometer in spherical defocus detection refers to the following steps: determining the dynamic range of the interferometer during spherical defocus detection as the maximum wave image difference value or the maximum number of rings during complete sampling of the detector, namely determining complete sampling of the detector; the requirements for complete sampling of the detector are: the interferogram can be fully resolved by the detector and the wave aberration corresponding to one interference fringe at the closest interference fringe on the interference pattern is equal to the wave aberration corresponding to the Nyquist frequency of the detector. The invention makes up the defect that the interferometer lacks a method for determining the dynamic range during the spherical defocus measurement, and improves the performance index of the interferometer. Reliable theory, simple method, accurate judgment and wide application range.

Description

Method for determining dynamic range of interferometer during spherical defocus detection
Technical Field
The invention belongs to the technical field of optical instruments and optical detection, and particularly relates to a method for determining a dynamic range of an interferometer during spherical defocus detection.
Background
According to the principle of superposition, the result of wave fusion has the property of reflecting the original state of the wave. When two beams of light of the same frequency are superimposed, they produce fringes that depend on their phase difference: when the phases are the same, a reinforcing fringe (or a circular ring) is generated, and conversely, a weakening fringe is generated, a fringe with intermediate intensity is generated between the two conditions, and the generated interference fringe can reflect the optical path difference of the two beams. The interferometer is an instrument for acquiring measurement information based on interference phenomena caused by superposition of waves, and is widely applied to measurement of micro displacement, refractive index and surface shape of optical elements in scientific research and industrial production. In scientific analysis, the interferometer is used for measuring the length and the surface shape of an optical element, and the precision can reach the nanometer level. The length measuring instrument is the length measuring instrument with the highest precision.
In the surface shape interferometry of optical elements, null detection is traditionally adopted, and is generally used for detection of spherical surfaces and planes. For an ideal plane, the detection system only has inclination, and the interference pattern is a group of parallel straight fringes at equal intervals; for an ideal spherical surface, when the detection system only has defocusing, the interference pattern is a group of concentric rings with unequal intervals. Therefore, the interference fringes are different in the detection of planar and spherical interference, which determines that the dynamic range is different even if the same interferometer is measuring different types of optical elements.
The dynamic range is the maximum wave aberration value of the interference measurement in the complete sampling and is determined by the number of interference fringes which can be resolved by a sampling detector in the interferometer. Dynamic range is an important measure of interferometer performance. The number of fringes that can be resolved, referred to in the description of some interferometers, is only equally spaced straight fringes, and is not mentioned in the case of interference rings. The interference ring is an interference phenomenon which often occurs in optical detection, especially in non-zero detection of aspheric surfaces, such as aspheric surface direct interference detection, sub-aperture stitching, partial compensation detection and the like. The dynamic range of interference detection in spherical defocusing is determined, so that the performance index of the interferometer can be perfected, and guidance can be provided for formulating an aspheric surface detection scheme.
Disclosure of Invention
The invention aims to provide a method for determining the dynamic range of an interferometer during spherical defocus detection, which is used for perfecting the performance index of the interferometer.
In order to solve the above technical problem, an embodiment of the present invention provides a method for determining a dynamic range of an interferometer during spherical defocus detection, where the dynamic range of the interferometer during spherical defocus detection refers to: determining the dynamic range of the interferometer during spherical defocus detection as the maximum wave image difference value or the maximum number of rings during complete sampling of the detector, namely determining complete sampling of the detector;
the requirements for complete sampling of the detector are: the interferogram can be fully resolved by the detector and the wave aberration corresponding to one interference fringe at the closest interference fringe on the interference pattern is equal to the wave aberration corresponding to the Nyquist frequency of the detector.
Wherein, the wave aberration equation of the spherical surface during defocusing interference detection is as follows:
Figure BDA0002405788780000031
wherein f' is the focal length of the spherical mirror to be measured; y is the aperture height of the spherical surface to be measured; delta is defocusing amount, namely the distance from the focus of emergent rays of the spherical lens of the interferometer to the spherical center of the spherical surface to be measured;
the interference fringes are closest at the edges of the interference pattern.
Wherein, the requirement of the wave aberration corresponding to the Nyquist frequency of the detector to the interference fringes is as follows: an interference circular ring at the edge of the interference pattern occupies 4 pixels of the detector, the corresponding wave aberration is half wavelength, and the defocusing amount at the moment is as follows:
Figure BDA0002405788780000032
wherein λ is a numberThe wavelength of a light source in the wave surface interferometer; f' is the focal length of the spherical mirror to be measured;
Figure BDA0002405788780000033
m is the pixel array of the detector; d is the caliber of the sphere to be measured.
Wherein, the dynamic range of sphere when out of focus is measured does:
maximum wave aberration
Figure BDA0002405788780000034
Maximum number of rings
Figure BDA0002405788780000035
Wherein, λ is the wavelength of the light source in the digital wave surface interferometer;
Figure BDA0002405788780000036
and M is the pixel array of the detector.
The technical scheme of the invention has the following beneficial effects: the invention makes up the defect that the interferometer lacks a method for determining the dynamic range during the spherical defocus measurement, and improves the performance index of the interferometer. Reliable theory, simple method, accurate judgment and wide application range.
Drawings
FIG. 1 is a light path diagram for spherical interference detection in the present invention;
FIG. 2 is an interference pattern of spherical detection when out of focus;
fig. 3 is an interference pattern when the plane detects the tilt.
Description of reference numerals:
1. a digital wavefront interferometer; 2. a standard spherical lens; 3. and (5) measuring the spherical surface.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
When the spherical surface is subjected to defocusing interference detection, the interference fringes are concentric rings, the interference pattern is just less than that of the whole detector, and the maximum wave aberration value or the maximum ring number when the detector completely samples is the dynamic range of the interferometer during the defocusing detection of the spherical surface. Based on the above, the invention provides a method for determining the dynamic range of an interferometer in spherical defocus detection, wherein the dynamic range of the interferometer in spherical defocus detection refers to: determining the dynamic range of the interferometer during spherical defocus detection as the maximum wave image difference value or the maximum number of rings during complete sampling of the detector, namely determining complete sampling of the detector;
the requirements for complete sampling of the detector are: the interferogram can be fully resolved by the detector and the wave aberration corresponding to one interference fringe at the closest interference fringe on the interference pattern is equal to the wave aberration corresponding to the Nyquist frequency of the detector.
The light path of the spherical interference detection is shown in fig. 1, which comprises a digital wave surface interferometer 1, a standard spherical lens 2 and a spherical surface 3 to be detected.
Firstly, a spherical aberration function during aspheric surface direct interference detection is deduced according to a three-level aberration theory, and then a wave aberration function of detection light is obtained according to the wave aberration theory.
When only defocus exists, assuming that defocus amount is Δ, the wave aberration function of the sphere detected in defocus obtained from the wave aberration equation is:
Figure BDA0002405788780000051
wherein f' is the focal length of the spherical mirror to be measured, and y is the aperture height.
The following can be obtained by deriving equation (1):
Figure BDA0002405788780000052
the wave aberration gradient is proportional to the aperture height, i.e. the wave aberration gradient is greatest at the aperture edge, where the interference fringes are densest. Assuming that the caliber of the round spherical surface to be detected is 2h, the interference pattern is fully distributed in the whole detector during sampling, and assuming that the pixel of the detector array is M N.
From the edge, the aperture d of the corresponding sphere inside the 2 nd ring is:
Figure BDA0002405788780000053
wherein M is the pixel array of the detector; d is the caliber of the sphere to be measured.
For ease of writing, let constant γ be:
Figure BDA0002405788780000054
the wave aberration between the outermost two rings of the interference fringes can be written as:
Figure BDA0002405788780000061
the optical path difference Δ W between two adjacent interference rings is λ/2, and the defocus amount Δ is known from equation (5),
Figure BDA0002405788780000062
wherein, lambda is the wavelength of the light source in the digital wave surface interferometer.
Substituting equation (6) into equation (1) yields a wave aberration function as:
Figure BDA0002405788780000063
when y is equal to h, D/2, the wave aberration is maximum,
Figure BDA0002405788780000064
conversion to the maximum number of rings can be expressed as:
Figure BDA0002405788780000065
equations (8) and (9) are respectively the maximum wave aberration and the maximum number of rings of the interferometer in the dynamic range during the spherical defocus detection, and it can be seen that the dynamic range of the interferometer is only related to the parameters of the sampling detector and is not related to the spherical parameters to be detected. It can be seen from equations (6) and (8) that the defocus amounts are different when the maximum measured wave aberration is reached by different spherical surfaces to be measured. If the interferometer lens is exactly matched with the spherical surface to be measured, the circular interference pattern is complete and is exactly filled in the detector, and the maximum defocusing amount and the maximum wave image difference value of the standard spherical lens of different F-number interferometers in the measurement of spherical defocusing energy complete sampling can be obtained, see table 1.
TABLE 1 maximum defocus and maximum wave aberration measurable by different interferometer standard ball lenses
Figure BDA0002405788780000071
It can be seen from table 1 that the larger the interferometer F number, the larger the defocus amount to reach just a full sample when the detector is timed. For a 640 x 480 detector array, the circular interferogram occupies the largest array of detector pixels at 480 x 480, and theoretically the interferometer can measure the largest wave aberration at 30.125 λ with approximately 60 interference circles. For a 1024 x 1024 detector array, the circular interferogram occupies the largest array of detector pixels at 1024 x 1024, theoretically the maximum wavefront aberration that the interferometer can measure is 64.1 λ, and the interference circles are about 128.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (4)

1. A method for determining the dynamic range of an interferometer in spherical defocus detection is characterized in that the dynamic range of the interferometer in spherical defocus detection refers to: determining the dynamic range of the interferometer during spherical defocus detection as the maximum wave image difference value or the maximum number of rings during complete sampling of the detector, namely determining complete sampling of the detector;
the requirements for complete sampling of the detector are: the interferogram can be fully resolved by the detector and the wave aberration corresponding to one interference fringe at the closest interference fringe on the interference pattern is equal to the wave aberration corresponding to the Nyquist frequency of the detector.
2. The method for determining the dynamic range of the interferometer in spherical defocus detection according to claim 1, wherein the wave aberration equation of the sphere in defocus interference detection is as follows:
Figure FDA0002405788770000011
wherein f' is the focal length of the spherical mirror to be measured; y is the aperture height of the spherical surface to be measured; delta is defocusing amount, namely the distance from the focus of emergent rays of the spherical lens of the interferometer to the spherical center of the spherical surface to be measured;
the interference fringes are closest at the edges of the interference pattern.
3. The method for determining the dynamic range of an interferometer in spherical defocus detection as claimed in claim 1, wherein the requirement of the interference fringes by the wave aberration corresponding to the Nyquist frequency of the detector is: an interference circular ring at the edge of the interference pattern occupies 4 pixels of the detector, the corresponding wave aberration is half wavelength, and the defocusing amount at the moment is as follows:
Figure FDA0002405788770000012
wherein, λ is the wavelength of the light source in the digital wave surface interferometer; f' is the focal length of the spherical mirror to be measured;
Figure FDA0002405788770000021
m is the pixel array of the detector; d is the caliber of the sphere to be measured.
4. The method of claim 1, wherein the dynamic range of the sphere in defocus measurement is:
maximum wave aberration
Figure FDA0002405788770000022
Maximum number of rings
Figure FDA0002405788770000023
Wherein, λ is the wavelength of the light source in the digital wave surface interferometer;
Figure FDA0002405788770000024
and M is the pixel array of the detector.
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